Physics 208: Electricity and Magnetism. Exam 3, Secs. 501–505 13 April 2006Instructor: Dr. George R. Welch, 301D Doherty Bldg, 845-1571Print your name neatly:Last name:First name:Sign your name:Please fill in your Student ID number (UIN): – –IMPORTANTRead these directions carefully:• There are 7 problems totalling 100 points. Check your exam to make sure youhave all the pages. Work each problem on the page the problem is on. Youmay use the back. If you need extra pages, I have plenty up front.• Indicate what you are doing! We cannot give full credit for merely writingdown the answer. Neatness counts! I will give generous partial credit if Ican tell that you are on the right track. This means you must be neat andorganized.• Each problem with its associated figure is self explanatory. If you must aska question, then come to the front, being as discrete as possible so as not todisturb others.• Put your name on each page it is asked for. You will lose credit if you fail toprint your name on each page it is asked for.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 1. 15 points.There is a uniform magnetic field B (pointing into the page) through a large rectangular regionof space. A wire carrying current I goes a distance a directly into the region of field, then bendsand comes back out at an angle θ from its original direction.Find the x and y components of the force on the wire. Express your answers in terms of B, I,l, θ, and numerical factors.Magnetic Field B(into the page)θRVIIaBe neat. Neatness helps. Work neatly.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 2. 20 points.Consider a long straight wire carrying a current I. Suppose that the wire has a circular cross-section of radius R, but that R is very small compared to the length of the wire. Assume that thecurrent flows through the wire uniformly distributed over the cross sectional area of the wire.(a) What is the magnetic field a distance r from the center of the wire, where r > R?(b) What is the magnetic field a distance r from the center of the wire, where r < R?NOTE: You must show your work and indicate what you are doing. I delib erately madethis easy, so you MUST show the process, not just the answer.If you work neatly I will find more partial credit for you!Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 3. 15 points.Consider two long straight parallel wires, one directly above the other, separated by a distance2d. One wire carries a current I. The other wire carries an unknown current in the oppositedirection. The magnetic field at the point S in the figure is zero. This point is a distance d abovethe wire with the known current.The figure shows a cross-section perpendicular to the wires.Known Current IdddPoint S2 dPoint QUnknown CurrentPoint P(a) Calculate the x and y components of themagnetic field at the point P which is directly be-tween the wires(b) Calculate the x and y components of themagnetic field at the point Q which is a distance√2 d to the right of the wire with the known cur-rent. Note: the y component has very simple ex-pression. Do not give me any complicated expres-sion. Simplify it.Make sure you are being neat. Working neatly will help you get it right.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 4. (20 points)A long straight wire carries a changing current i(t). A rectangular loop of wire is placed nearthe long straight wire. The loop is made of a resistive material and the total resistance of the loopis R. The distance from the long straight wire to the near edge of the loop is c, and the width andheight of the loop are a and b respectively. All these dimensions (a, b, and c) are much smaller thanthe length of the long straight wire. The situation is shown in the Figure.i(t)bc aSuppose that the current in the long straight wire var-ries according toi(t) =I0µ1 −tτ¶0 < t < τ0 t > τCalculate the magnitude and direction (clockwise orcounter-clockwise) of the current induced in the loop, for0 < t < τ.Work neatly! If you are neat, I can read what you did and maybe find more points for you.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 5. (10 points)For each of the following 5 cases (a)–(e) there is a loop of wire denoted A near another wirethat is conducting some current. In each case, current is induced in loop A. Indicate whether theinduced current is clockwise or counter-clockwise.Please only write either “clockwise” or “counter-clockwise” as the answer for each case.Points: 5 correct = 10 points, 4 correct = 7 points, 3 correct = 3 points.I increasingAAnswer:I decreasing(a)(b)AAnswer:(c)Answer:I increasingI increasingAAAnswer:Answer:(d)(e)I constantLoop moving to rightAPrint your name:Physics 208: Electricity and Magnetism, Exam 2Problem 6. (5 points)The following laws were found empirically and formed the basis for understanding the interactionof charges and currents.Gauss:I~E · d~A =Qinside²0I~B · d~A = 0Amp`ere:I~B · d~l = µ0IenclosedFaraday:I~E · d~l = −ddtΦBIndicate which one of these laws Maxwell changed in advance of his prediction of electromagneticwaves, and write down the corrected version of that law.You should be neat. You are more likely to get it right if you work neatly.Print your name:Physics 208: Electricity and Magnetism, Exam 2Problem 7. (15 points)Consider the circuit shown below. Initially, both switches are open.R1R2VL1S2S(a) Suppose the switch S1is closed. What is the current through R2immediately after thishappens?(b) Now supp ose we wait a long time after closing switch S1. What is the current through R2then?(c) Now, after waiting a long time as above, suppose we close switch S2. What is the currentthrough R2immediately after that?(d) Now, write an equation for the current through R2as a function of time, taking t = 0 to bethe moment S2is closed (in part c).Working neatly will help you think about what you are